FORTUNE — After almost three years of President Obama’s leadership, the economy is still dismal and Americans are angry. In a speech on unemployment and the national debt delivered from the Rose Garden last week, the president seemed fired up too.

The president’s tone was a marked departure from his usual, cool-headed demeanor. He sounded combative, and people noticed. The Huffington Post even recapped the speech in an article entitled “Obama Finally Grows a Pair.”

Anger, it turns out, can be a very useful emotion for leaders. But expressing anger during an event such as a public speech is a tricky tactic that, when executed poorly, can cause a backlash.

But the worst-case response to a tone change like this one is to hear crickets, says Virginia Healy-Tangney, a lecturer at MIT’s Sloan School of Management. After all, there’s nothing more frustrating than getting no response when you’re angry.

Strong language can function as an effective wake-up call. Earlier this year, Nokia CEO Stephen Elop got the world to pay attention to his company again by the way he framed its current crisis. Elop said Nokia (NOK) was like a person standing on a burning platform and would have to jump into icy water to save itself.

Leaders in crisis mode sometimes have to convey anger or aggressiveness to appear relevant, says Healy-Tangney. She remembers when Ronald Logue, then-CEO of State Street, her previous employer, spoke to the company about the massive layoffs he was forced to make because of the financial crisis. He was angry about the situation, and he conveyed it. Despite hearing tough news, employees responded well to the speech, Healy-Tangney says.

In a way, we are hard-wired to respect an angry leader, even if we don’t admit it. In a 2001 study published by Stanford organizational behavior professor Larissa Tiedens, participants watched videos of Bill Clinton responding to the Monica Lewinsky scandal. One group viewed a video of a remorseful Clinton and the other saw a clip of the former president responding angrily. Then, researchers measured how the viewers rated Clinton’s leadership ability. People who saw video clips of Clinton expressing anger rated him better fit to lead, Tiedens observed.

Of course, after you get people’s attention or respect with an outburst, then comes the hard part: backing up what you say. Elop needs to deliver results after shifting strategy at Nokia, and a CEO making massive layoffs like Logue needs to actually turn the company around.

“In order to have dominance, there must be a tacit threat,” says Robert Livingston, a professor of management at Northwestern’s Kellogg management school. “If you’re a bully and people don’t think that you can beat them up, they’re not going to give you the lunch money.”

And staying angry for too long has its risks. For one, people can only stomach so much negativity. Secondly, when an audience listens to an emotional leader speak, they tend to interpret the message as personal, more about the leader’s ego than the people they’re addressing, says Healy-Tangney. While sharp words can be an effective call for attention, perceived selfishness is a huge turn-off.

Of course, the president’s tone has changed in the context of a complicated political balance. We’re coming up on election time, and he has been repeatedly stymied by congress. Every move the president makes is extremely calculated, and a tone change is no different. This recent speech was a chess move, says Tom Davis, former chairman of the National Republican Congressional Committee, and a pretty predictable one. Obama will oscillate between his stately, presidential self and a politician angered by the issues, Davis says. “It’s easy to criticize him, sitting on the sidelines, but this is straight from a playbook.”

Now that people are listening, getting angry may look like a good move, but it will only pay off in the long run if he can execute.